November 4 (Sat), 2017 (Sat) 11:30--12:30, 15:20--16:20 Graduate School of Mathematical Sciences The University of Tokyo, Tokyo, Japan |

Martin Hairer

(Imperial College London)

(Imperial College London)

**Abstract**

We give a survey of recent result in probability theory regarding scaling limits of systems from statistical mechanics, as well as the universality of the behaviour of such systems in so-called cross-over regimes. It transpires that some of these universal objects are described by singular stochastic PDEs. We then give a survey of the recently developed theory of regularity structures which allows to build these objects and to describe some of their properties.